 This original result due to Wigner has been extended in several aspects. Grenander [1]} proved the empirical spectral distribution converges to \(\mu _{\operatorname{sc}}\)  in probability. Arnold [2]}, [3]} further improved this result by showing the empirical spectral distribution converges to the semicircular law almost surely. We remark that the matrix ensembles underlying (REF ) can be generalized beyond those originally considered by Wigner and refer the reader to [4]} and [5]} for excellent surveys on the rich and rapidly developing field of spectral analysis of large random matrices.
